Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents

This paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least...

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Main Authors: Khaled Kefi, Nasser S. Albalawi
Format: Article
Language:English
Published: AIMS Press 2025-02-01
Series:AIMS Mathematics
Subjects:
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2025207
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author Khaled Kefi
Nasser S. Albalawi
author_facet Khaled Kefi
Nasser S. Albalawi
author_sort Khaled Kefi
collection DOAJ
description This paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least three weak solutions under general assumptions on the weight function and the nonlinearity. This result has wide applicability, extending existing theories on quasilinear elliptic equations.
format Article
id doaj-art-74c8a2941ac64382be4736d3e17a4ace
institution OA Journals
issn 2473-6988
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publisher AIMS Press
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series AIMS Mathematics
spelling doaj-art-74c8a2941ac64382be4736d3e17a4ace2025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-02-011024492450310.3934/math.2025207Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponentsKhaled Kefi0Nasser S. Albalawi1Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi ArabiaDepartment of Computer Sciences, Faculty of Computing and Information Technology, Northern Border University, Rafha, Saudi ArabiaThis paper explores the multiplicity of weak solutions to a class of weighted elliptic problems with variable exponents, incorporating a Hardy term and a nonlinear indefinite source term. Using critical point theory applied to the associated energy functional, we establish the existence of at least three weak solutions under general assumptions on the weight function and the nonlinearity. This result has wide applicability, extending existing theories on quasilinear elliptic equations.https://www.aimspress.com/article/doi/10.3934/math.2025207variational methodshardy inequalitydegenerate $ p(x) $-laplacian operators
spellingShingle Khaled Kefi
Nasser S. Albalawi
Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
AIMS Mathematics
variational methods
hardy inequality
degenerate $ p(x) $-laplacian operators
title Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
title_full Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
title_fullStr Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
title_full_unstemmed Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
title_short Three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
title_sort three weak solutions for degenerate weighted quasilinear elliptic equations with indefinite weights and variable exponents
topic variational methods
hardy inequality
degenerate $ p(x) $-laplacian operators
url https://www.aimspress.com/article/doi/10.3934/math.2025207
work_keys_str_mv AT khaledkefi threeweaksolutionsfordegenerateweightedquasilinearellipticequationswithindefiniteweightsandvariableexponents
AT nassersalbalawi threeweaksolutionsfordegenerateweightedquasilinearellipticequationswithindefiniteweightsandvariableexponents